Answer to Question #102860 in Mechanics | Relativity for Elia

Question #102860
A special phototype model aeroplane of mass 400g has a control wire 8cm long attached to its body the other end of the control line is attached to afixed point .when aeroplane flies with its string wing horizontal in a horizontal circle 30degree above the horizontal .draw a diagram showing the four exerted on a plane and determine. a)Tension in the control wire b)the lift on the plane ( g=10m/s pie^2=10)
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Expert's answer
2020-02-13T08:54:26-0500


Write forces according to Newton's second law. Since the airplane is moving along a circumference with radius equal to the horizontal projection of the string, the net force is the centripetal force. Therefore:


Ox:T cos30=mv2r=mv2l cos30, Oy:T sin30mg=0.Ox:T\text{ cos}30^\circ=m\frac{v^2}{r}=m\frac{v^2}{l\text{ cos}30^\circ},\\ \space\\ Oy:T\text{ sin}30^\circ-mg=0.

Solve that system of equations by expressing tension from the second equation first:


T=mgsin30=7.84 N.T=\frac{mg}{\text{sin}30^\circ}=7.84\text{ N}.

The speed of the plane:

v= cos30Tlm= cos30glsin30=1.1 m/s.v=\text{ cos}30^\circ \sqrt{\frac{Tl}{m}}=\text{ cos}30^\circ \sqrt{\frac{gl}{\text{sin}30^\circ}}=1.1\text{ m/s}.


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